Abstract
Let E be an ample vector bundle on a projective manifold X , with a section vanishing on a smooth subvariety Z of the expected dimension, and let H be an ample line bundle on X inducing a very ample ample line bundle H Z on Z . Triplets (X,E,H) as above are classified assuming that Z , embedded by | H Z | , is a variety of small degree with respect to codimension.
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